AP EAMCET · PHYSICS · Units and Dimensions
The time period of revolution of a satellite ( T ) around the earth depends on the radius of the circular orbit ( R ), mass of the earth (M) and universal gravitational constant (G). The expression for T , using dimensional analysis is ( K is constant of proportionality)
- A \(\mathrm{K} \sqrt{\frac{\mathrm{R}^2}{\mathrm{GM}}}\)
- B \(K \sqrt{\frac{R}{G M}}\)
- C \(\mathrm{K} \sqrt{\frac{\mathrm{R}^3}{\mathrm{GM}}}\)
- D \(\mathrm{K} \sqrt{\frac{\mathrm{R}^3}{\mathrm{GM}^2}}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{K} \sqrt{\frac{\mathrm{R}^3}{\mathrm{GM}}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \mathrm{T} \propto \mathrm{R}^{\mathrm{a}} \mathrm{M}^{\mathrm{b}} \mathrm{G}^{\mathrm{c}} \Rightarrow \mathrm{T}=\mathrm{k} \mathrm{R}^{\mathrm{a}} \mathrm{M}^{\mathrm{b}} \mathrm{G}^{\mathrm{c}} \\ &…
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